@GreC_89 Let me explain the technicality.
R34 or Rule 34 refers to the Rule of The Internet number 34 that states "If it exist, there is porn of it."
This rule dictate that anything that exist in the internet, no matter the form and the state of their sentience, there will a porn of it. Since this went into effect on something HAD to exist first in the Internet, any porn that refer to it fall into Fan Art or Parody Catagory
Now, Doujin (or the more exact term is Doujinshi since doujin mean a group who share the same interest but eveywhere outside japan keep switching between the two term to mention the same thing), in it's truest form, refer to a self published art media (magazine, comic, manga, novels, songs, etc) that is created by a group of enthusiast or just a single person. It cover original contents and parody, but in the west, when mentioning doujin, they usually mean the original one instead of the parody.
So what i mean by my comment is that i had a faint rememberance of an erotic doujin that is not a parody of existing work with the exact, if not similar, plot of what Ailamus said.